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Pribnow, Kinoshita & Stein - 1 - ODP Heat Flow Report

Daniel PribnowMasataka KinoshitaCarol Stein

Thermal Data Collection

and Heat Flow

Recalculations for

Ocean Drilling Program

Legs 101-180


Institut für

Geowissenschaftliche Gemeinschaftsaufgaben (GGA)

Thermal Data Collection and

Heat Flow Recalculations for

Ocean Drilling Program Legs 101-180

Daniel F.C. Pribnow

Institute for Joint Geoscientific Research GGA30655 Hannover, Germany

[email protected]

Masataka KinoshitaSchool of Marine Science and Technology, Tokai University

Shimizu-City, 424-8620, [email protected]

Carol A. SteinDept. of Earth and Environmental Sciences

University of Illinois at ChicagoChicago, IL 60607-7059, USA

[email protected]

Projekt: DFG Pr471/2

Datum: 6. Oktober 2000Archiv Nr.: 0 120 432

mailto:[email protected]




In memory of Marc G. Langseth

Marc Langseth spent many months at sea making heat flow measure-ments both at and under the sea floor on ships such as Glomar Chal-lenger and JOIDES Resolution. He organized this project but passed

away shortly after this work was initiated.

We will miss him as a colleague and a friend.

P

Abstract. In this report the geothermal measurements made with temperature probes onthe JOIDES Resolution during legs 101-180 are reanalyzed in a standard systematic manner.Sediment temperatures were measured on 53 of the first 80 Ocean Drilling Project Legs. 205of the 475 sites have reliable data. For 22% of sites with reliable values, however, heat flowdata were not reported in the Initial Results volumes. A total of 993 reliable temperaturemeasurements yields an average of 4.8 measurements per site. Most temperature measure-ments were between 20 to 250 mbsf, and the deepest depth in this study is 550 mbsf. Avail-able thermal conductivity data for these 205 sites were corrected for in-situ conditions. Heatflow values, calculated using the Bullard method, range from 5 mW m-2 to 13 W m-2. Tem-perature, thermal conductivity, and heat flow data presented in this report are available fromthe included CD.

1. IntroductionGeothermal measurements are important data needed to study the Earth's processes. The

values measured on the JOIDES Resolution during Ocean Drilling Program (ODP) Legs 101-180 reflect heat transfer from the interior of the Earth, oceanic lithosphere evolution, conti-nental margin formation, subduction, and hotspot volcanism. In addition, these data are usedto examine more shallow processes associated with fluid flow and gas hydrate formation. Tocalculate heat flow, temperatures with depth and the thermal conductivity of the material inwhich the temperatures are measured must be known. If the thermal conductivity is constantover the depths over which the temperatures are measured and if heat transfer is essentiallyvertical and conductive, then heat flow can be calculated using Fourier's Law. In this case,

F

180˚180˚ 0˚

ribnow, Kinoshita & Stein - 4 - ODP Heat Flow Report

igure 1: Locations of heat flow measurements from ODP Legs 101-180.

180˚ 210˚ 240˚ 270˚ 300˚ 330˚ 0˚ 30˚ 60˚ 90˚ 120˚ 150˚ 180˚

-60˚

-30˚

0˚

30˚

60˚

210˚

240˚

270˚300˚

330˚0˚

30˚

60˚

90˚

120˚

150˚

180˚

210˚

240˚270˚

300˚

330˚ 30˚

60˚90˚

120˚

150˚

180˚


heat flow is the product of the vertical gradient of the temperature, which is generally positivedownwards (temperature increases with depth), and the measured or estimated thermal con-ductivity of the material. If the thermal conductivity changes with depth, heat flow may becalculated with the Bullard method. In this report, we first review the equipment and methodsused to collect and analyze the thermal conductivity and temperature data on the first 80 ODPlegs. We then discuss the method used to calculate the heat flow. Next, we report the heatflow for the 205 measurements (Figure 1). Last, we describe how this data can be accessed.We have examined only data from probes inserted into sediments and not from downhole log-ging. The tectonic implications of these heat flow data will be discussed in a manuscript cur-rently in preparation.

2. Methods2.1 Thermal Conductivity Shipboard Instrumentation

Thermal conductivity measurements in thecore laboratory on JOIDES Resolution are madeusing the transient line-source (needle-probe)technique (von Herzen and Maxwell, 1959). Theline-source is a cylindrical probe, 2 mm in di-ameter and 70 mm long, that contains a heatingwire and a thermistor. The line-source is heatedwith constant power. Thermal conductivity is cal-culated from the temperature-time response to theline-source, providing a two-dimensional valuefor a plane perpendicular to the needle axis. Ship-board measurements are made by pushing theneedle-probe horizontally through the core-linerinto soft sediments (Figure 2; for details of anisot-ropy effects, see Pribnow et al., 2000). Two de-vices are currently available in the core lab.Thermcon-85

This unit was purchased from Woods Hole Oceanogrphic Institution and the softwarewas developed by ODP in 1991. Up to five needle-probes can be used simultaneously (Daviset al., 1992). The device is calibrated regularly by measuring standards with known conduc-tivity. Precision and accuracy are about 5%. During the data processing, the operator has tochoose manually a time interval from which the thermal conductivity is calculated. The resultsare dependent on this chosen interval and therefore reproduceability may vary from operatorto operator.TK04

ODP purchased TK04 in late 1995 and deployed it permanently on the ship during Leg168 in 1996 (Davis et al., 1997a). A calibration is not required. The main advantage of theTK04 system is a processing algorithm which ensures that only results of physical signifi-cance are considered. The critical choice of time interval for calculation of conductivity isaccomplished automatically. The algorithm determines the optimal interval. In addition, thesolutions can be judged in great detail and the data can be re-processed with different bound-ary parameters. The precision using extended evaluations is better than 2%. For routineevaluations of repeated measurements, the accuracy is about 5%.

core linerline-source

core

Figure 2: Scheme of the thermal conductivitymeasurements with a shipboard line-source.For clarity, the core is not shown and the coreliner is cut open. The thin, dark planes repre-sent horizontal bedding in the sediment core.The thick, light-gray disk indicates the planefrom which the line-source scans the thermalconductivity.


2.2 Sediment Temperatures ShipboardInstrumentation

To infer equilibrium temperatures of thesediments, prior to pertubation by drilling, a sensoris pushed into the sediments just below the bottomof the hole and ahead of the drill bit. One system,the Advanced Piston Corer (APC) tool measuresin-situ sediment temperatures during regular pis-ton-coring operations (Davis et al., 1992; Fig. 3).The APC contains a miniature programmable re-corder and battery pack designed to fit inside anannular cavity of a coring shoe. Two steel prongsextend from the base of the frame, one of whichcontains a platinum resistance-temperature device.The APC also has been referred to as the von Her-zen, ADARA (processing software company) orHPC (Hydraulic Piston Corer) temperature tool.The APC was first used during DSDP Leg 86 (Ho-rai and von Herzen, 1985) and an improved ver-sion was introduced during ODP Leg 110 (Davis etal., 1992).

The Water Sampler Temperature Probe(WSTP) is a hybrid of two other tools, the UyedaTemperature Tool (Yokota et al., 1980) and theBarnes Fluid Sampler (Barnes, 1979). The firstgeneration, also referred to as T Probe or UyedaProbe, was used until ODP Leg 116. The secondgeneration of WSTP became available during ODPLeg 110 with improved sampling capabilities and astouter temperature probe (Barnes, 1988). A thirdversion of this tool was introduced during Leg 139in anticipation of encountering extremely corrosivefluids at high temperatures. The original UyedaTemperature Tool had a thin, stainless-steel probewhich was pushed ahead of the bit into the undis-turbed sediments at the bottom hole. The secondgeneration tool had a probe tip with a minimumdiameter of 1.3 cm which extended 8.3 cm past a5.1 cm diameter pore-fluid filter block. The newWSTP includes a temperature tip which is slightlylonger (Fig. 4; after Davis et al., 1992). Individualtemperature measurements have a nominal resolu-tion of about 0.02 K (near room temperature);resolution falls off with increasing temperature.

Regardless of which equipment is used to measure temperatures, as the probe is insertedinto the sediments it is initially heated due to friction and cools towards the equilibrium tem-perature. Processing the data to infer the equilibrium temperature involves careful and some-what subjective fitting of measured temperatures to expected temperature-time curves. Thetheory behind APC measurements is described by Horai and von Herzen (1985). The theoreti-

Figure 4: Configuration of the WSTP.

Figure 3: Two generations of the APC tempe-rature tool (Horai and von Herzen, 1985;Davis et al., 1992).

Pribnow, Kinoshita & Stein - 7

cal cooling curve after the frictional heatingof the APC is obtained by solving the ther-mal conduction equation for composite cir-cular cylinders. The temperature of the metalcylinder is modelled as radially isothermalafter several tens of seconds because of itshigh thermal conductivity. The currentlyused software TFIT was developed by JamesCraig and Adara Systems Ltd., based onsoftware by Keir Becker (APCFIT).

For the Davis-Villinger TemperatureProbe (DVTP; Davis et al., 1997a; 1997b),the theoretical cooling curve is based on anidealized radial heat conduction model thatsimulates the thermal decay of the instru-ment following frictional heating from toolinsertion. A segment of temperature versustime data from each deployment is comparedto a theoretical decay function, and thepenentration time of the tool is shifted rela-tive to the model in order to get a best statis-tical (least-squares) fit. The trend of the observa

To estimate undisturbed in-situ temperawere developed and are supported by ODP. (TFIT) can interactively determine in-situ tempters; penetration time (or the origin time, tor), tculate equilibrium temperatures, and in-situ thexample of temperature recorded by the APC tto minimize the fitting error (Figure 6). Howevtf also significantly affect the results. Selectionparameters is made arbitrarily by shipboard salthough they may keep these values constant dleg.

To test sensitivities of these parameters ttimated equilibrium temperatures, fits were various sets of time intervals ti and tf. Resultssented as contours of both equilibrium temperatheir standard errors. Figure 7 shows typical exahigh and low quality data. For high quality equilibrium temperatures are almost constan0.1 °C for a moderate range of selected time On the other hand, the estimated temperatures v1 °C with varying time intervals for low qualitshould be noted that, even for bad quality, temvs. time plots appears as good as others. Thus, important to maintain the time intervals throughout the analysis.

30

25

20

15

10

5

Tem

pera

ture

(°C

)

10005000-500Time after penetration (sec)

Pene

trat

ion

Mud

line

Pull

out

ti tf

Fig. 5: Example of APC tool measurements.

- ODP Heat Flow Report

tions is extrapolated to infinite time.tures, several versions of reduction softwareSome of them, including the newest versioneratures by manually specifying four parame-ime interval (initial ti and final time tf) to cal-ermal conductivity. Figure 5 shows a typicalool. The origin time is automatically adjusteder, ti and of thesecientists,

uring one

o the es-done for are pre-tures andmples ofdata, thet withinintervals.ary up toy data. Itperature

it is veryconstant

8

7

6

5

4

Equi

libriu

m T

empe

ratu

re(°

C)

-100 -50 0 50 100Origin time(tor) shift(sec)

0.120.080.04

RM

S R

esid

ual(°

C)

Bestfit value

30

25

20

15

10

5

Tem

pera

ture

(°C

)

5004003002001000

Time after penetration (s)

-15-10

-505

10

Res

idua

l(mK

)

Fig. 6: Results of equilibrium tempe-rature fitting.


Based on these estimations, we keptthe time intervals ti and tf at 210 s and 540 safter penetration, respectively. For this inter-val most estimated temperatures are withinthe flat region in the contour diagram (Figure7). However, for a few cases where the fric-tional decay is extremely large, we changedthese values because they produced unrealis-tic equilibrium temperatures. Instead, weused a longer interval. The new results matchwithin a few tenth °C, although in somecases both results differ by up to 0.5 °C ormore.

Fig. 7: Typical examples of high (top) and low(bottom) quality records.


2.3 Heat Flow Calculation2.3.1 The Bullard Method

The Bullard (1939) method was introduced to calculate heat flow from borehole datawhen there is significant variation of thermal conductivity within the depth range over whichthe temperatures have been measured. It assumes a linear relation between temperature T andthermal resistance Ω of the sediments:

)()( 0 zqTzT Ω⋅+= (1)

where z is depth, T0 is the surface temperature (z = 0), q is heat flow, and the thermal resis-tance is:

=

−−≈=

z I

i i

ii zzz

dzz0 1

1

)()(

λλΩ (2)

with zi and zi-1 as bottom and top depths, respectively, of a horizontal layer with thermal con-ductivity λi. I is the number of layers between the surface and depth z. If Ω(z) is plotted versusT(z) in the so-called Bullard plot, a linear regression allows estimation of the surface tem-perature (T0) from the intercept with z = 0 and of heat flow (q) from the slope (eq. 1). A Bul-lard plot will be linear if conditions are conductive, steady state, and there are no internal heatsources.2.3.2. Thermal Resistance

To calculate heat flow with the Bullard method (eq. 1), the thermal resistance Ω is re-quired at the depths of available temperature values zT,j which are typically not coincidentwith the depths of measured thermal conductivity values zλ,k. By transforming thermal con-ductivity values from discrete depths (λk) into continuous profiles λ(z), thermal resistance (Ωj)can be calculated for the depths of temperature measurements (Τj). In this study, three differ-ent approaches for continuous conductivity profiles are used, based on the characteristics ofthe individual sites: (1) the average approach, where no systematic trend of thermal conduc-tivity with depth is observed; (2) the linear approach, assuming a systematic and linear varia-tion of thermal conductivity with depth; and (3) the porosity approach, based on the assumtionof exponentially decreasing porosity with depth and the geometric mean model as a mixinglaw for sediment-matrix and pore-water thermal conductivity.

2.3.2.1 The average approach is based on the assumption that there is no systematicvariation of thermal conductivity with depth. It is also appropriate for situations where thenumber of measurements is insufficient to characterize possible systematic variations prop-erly. The continuous profile is a constant value, λAVG, calculated from all thermal conductivitymeasurements, λk:

=

⋅=K

kkAVG K 1

1 λλ (3)

Based on this approach and solving the integral in equation (2), the thermal resistance, ΩAVG,for the depth, zT,j, of the jth temperature value, Tj, is calculated with:

AVG

jTjAVG

zλ

Ω ,, = (4)


2.3.2.2 The linear approach is based on the assumption that there is a systematic and lin-ear variation of thermal conductivity with depth. For example, a reduction of porosity withdepth due to compaction results in a systematic increase of conductivity with depth. Alterna-tively, increasing temperature with depth results in a systematic conductivity decrease withdepth. The continuous profile is represented by a straight line,

zzLIN ⋅+= Γλλ 0)( , (5)

calculated from a linear regression of all thermal conductivity measurements, [λk, zλ,k]. Basedon this approach and solving the integral in equation (2), the thermal resistance, ΩLIN, for thedepth, zT,j, of the jth temperature value, Tj, is calculated using the results of the linear regres-sion, λ0 (calculated surface thermal conductivity) and Γ (slope), with:

ΓλΓλ

Ω)ln()ln( 0,0

,

−⋅+= jT

jLIN

z(6)

2.3.2.3 The porosity-related approach is based on two assumptions resulting in a sys-tematic and non-linear increase of thermal conductivity. It is especially appropriate for sea-floor sediments where porosity can change rapidly in the upper section.1) Due to compaction, porosity φ decreases exponentially with depth;

−⋅=

Dzz exp)( 0φφ , (7)

where φ0 is the porosity at z = 0 and D is the characteristic depth.2) The bulk thermal conductivity, λCOM(z), is the geometric mean of the fluid conductivity, λf,and the matrix conductivity, λm, weighted with the porosity, φ(z), and the matrix volume,(1-φ(z)), respectively;

)(1)(()( zm

(z)fCOM )z φφ λλλ −⋅= (8)

Based on these assumptions, the thermal resistance, ΩCOM, for the depth, zT,j, of the jth tem-perature value, Tj, is calculated using the thermal conductivity of water λf=0.6 W m-1 K-1, andλm, φ0, D from a least square fit of all thermal conductivity measurements [λk, zλ,k] with k=1,K. The integral in equation (2) becomes

with 0φ

λλ −

=

m

fA : dzAjTz

Dz

mjCOM

−=,

0

exp

, )(1λ

Ω (9)

The solution of this integral leads to the exponential intergral function Ei

−⋅−⋅⋅−=

Dz

AEiAEiAD JT

mjCOM

,, exp)ln())(ln(

λΩ (10)

with: = dx

xaxaxEi exp)( .


A reasonable approximation of ΩCOM can also be obtained by using the least square fit directlyto calculate the thermal resistance. λCOM(zi) is calculated using equations (7) and (8) with theresults of the least square fit, λm, φ0, D, and λf=0.6 W m-1 K-1 for regular depth intervals be-tween the surface, z = 0, and the depth, zT,J, of the last temperature measurement, Tj,

JTJT

i zI

ziz ,

,0 ≤⋅=≤ , i = 1, I (11)

The thermal resistance, ΩCOM, for the depth, zT,j, of the jth temperature value, Tj, is then cal-culated based on the discrete step function approach

jTi zz withi all for ,≤ = λ

=ΩN

1i iCOM

ij,COM )z(

z(12)

The number of used depth intervals, I, controls the accuracy of this approximation.The choice of the appropriate method to obtain a continuous conductivity profile de-

pends on the characteristics of the individual conductivity measurements with depth. Figure 8shows examples for the three continuous thermal conductivity approaches. In the first case(Hole 784A), the average approach is most appropriate. The amount and scatter of the indi-vidual conductivity data do not indicate any systematic variation with depth. The trend of a

0.6 0.8 1.0 1.2

0

50

100

150

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250

300

thermal conductivity (W m-1 K-1)

dept

h (m

bsf)

Leg 125 Hole 784A

0.6 1.0 1.4 1.8 2.2

0

50

100

150

200

250

300

350

400


Leg 122 Hole 763A

0.6 0.8 1.0 1.2 1.4 1.6 1.8

0

50

100

150

200


Leg 120 Hole 747A

Figure 8: Examples for continuous thermal conducitivity approaches. Individual laboratory measurementshave been corrected for in-situ conditions (see text). Dotted lines: average approach (eq. 3), dashed lines:linear approach (eq. 5); solid line: porosity approach (eq. 8);

Left: Hole 784A, average: 0.91 W m-1 K-1, standard deviation of average (sdev): ±0.13 W m-1 K-1, inter-cept of linear regression (λ0): 0.89 W m-1 K-1, slope of linear regression (Γ): 0.13 W m-1 K-1 km-1;

Center: Hole 763A, average: 1.46 W m-1 K-1, sdev: ±0.23 W m-1 K-1, λ0: 1.21 W m-1 K-1, Γ: 1.52W m-1 K-1/km;

Right: Hole 747A, average: 1.30 W m-1 K-1, sdev: ±0.15 W m-1 K-1, λ0: 1.15 W m-1 K-1, Γ: 1.84W m-1 K-1 km-1, porosity approach: 1.38 W m-1 K-1 matrix conductivity, 70% porosity at sea floorand 21.5 m characteristic depth.


linear fit is well within the standard deviation of the average (sdev). Thus, the continuous ap-proach for this case is 91.0)( =zλ W m-1 K-1.

The second example in Figure 8 (Hole 763A) shows a clear linear trend of conductivitywith depth. The average approach is not appropriate, as indicated by the large sdev. In thiscase, the continuous approach is zz ⋅⋅+= −31052.121.1)(λ W m-1 K-1.

For the third example (Hole 747A), the porosity approach is most appropriate to repre-sent a continuous thermal conductivity profile, especially in the upper 40 mbsf. The leastsquares fit of the data yields reasonable values: 1.38 W m-1 K-1 matrix conductivity, 70% po-rosity at the sea floor and 21.5 m as the characteristic depth (D) for an exponential decrease ofporosity. Neither the average nor the linear approach represent the individual conductivitydata appropriately. Here, the continuous approach is )()( 38.161.0)( zzz φφλ ⋅= W m-1 K-1, withporosity 5.21/exp70.0)( zz −⋅=φ . For the case of step-wise variations due to lithologicalchanges, the approaches are performed for each section separately.2.3.3. Thermal Conductivity Corrections

Thermal conductivity is dependent on temperature and pressure (e.g., Clark, 1966; Clau-ser and Huenges, 1995). Laboratory measurements thus need to be corrected for appropriatein-situ conditions. In this study, we use the correction of Hyndman et al. (1974):

⋅−

+⋅

⋅++⋅=

1004)(

10018291)(,

labwlabTP

TzTzzz ρλλ (13)

where λP,T(z) is the in-situ thermal conductivity at depth z (mbsf), λlab is the value measured inthe laboratory, zw is water depth, ρ is mean sediment density (g cm-3), T(z) is the in-situ tem-perature, and Tlab is sample temperature during the thermal conductivity measurement. Thiscorrection considers pressure (center term) and temperature (right term) effects based onstudies by Ratcliffe (1960). The valid temperature range is 5 to 25 °C, which is appropriate formost but not all applications in this study. Sediment density was set to 1.8 g cm-3 for all cal-culations. For sites with temperatures exceeding 25 °C, the correction was still applied forreasons of consistency and the lack of alternatives. These sites with questionable in-situ cor-rections are marked in the final heat flow table.


2.3.4. Heat ProductionRadiogenic heat production is caused by transforming kinetic energy of particles, which

are emitted during the decay of uranium, potassium and thorium, into heat. The produced heatcontributes cummulatively to heat flow through the crust. Nearer to the surface, the totalthickness of the heat producing layer increases and hence there is an increase in the total heatflow with depths nearer to the surface, and thus, a non-linear Bullard plot.

To assess the significance of marine sediment heat production for heat flow throughoceanic crust, we used gamma-ray spectra from Hole 948C (Leg 156) measured in the bore-hole (Leg 156 IR volume) and from cores (Blum et al., 1997) to calculate the heat productionrate (Rybach, 1976). Figure 9 shows that the reduction of heat flow within 600 m is less than0.5% of the sea floor value. Hence, effects of the radiogenic heat production in marine sedi-ments are not included in this study.

0 5 10 15 20 25 30 35

0

100

200

300

400

500

600

temperature (oC)

dept

h (m

bsf)

Temperature

0 0.5 1 1.5 2 2.5

Heat Production

A (µW/m3)

drillpipe

0 100 200 300 400

78.7 78.8 78.9 79.0

ΣA*z (µW/m2)

heat flow (mW/m2)

heat

flow

at s

ea fl

oor

Figure 9: Effect of heat production on heat flow for Hole 948C, Leg 156. Left: sediment temperatures; cen-ter: heat production rate (A) calculated from gamma-ray spectra measured in the borehole (line) and fromcores (circles), low values in the upper 80 mbsf are measured in the drill pipe; right: the reduction of seafloor heat flow (calculated in this study) due to a cummulative contribution of heat production (ΣA*z) is lessthan 0.5% over 600 m.

P

2.3.5. Heat FlowTo calculate heat flow, the final step is a linear regression of the thermal resistance vs.

temperature data (eq. 1). A typical example from this study is shown in Figure 10 for Hole747A (Leg 120). Using the appropriate approach for the continuous thermal conductivity pro-file (Section 2.3.2; Figure 8) and the resulting thermal resistance, improves the linearity of theBullard Plot. This means that the decrease of temperature gradient with depth can be related toa thermal conductivity increase if the best fit for individual measurements is used. The finalresult is derived from the linear regression of all data (49 mW m-2).

0 2 4 6 8

0

20

40

60

80

100

120

140

temperature (oC)

dept

h (m

bsf)

0 20 40 60 80 100

0

20

40

60

80

100

120

140

thermal resistance (m2 K W-1)

dept

h (m

bsf)

Leg 120 Hole 747A

0 2 4 6 8

0

20

40

60

80

100

120

temperature (oC)

ther

mal

resi

stan

ce (m

2 K W

-1) 60 mW m-2

37 mW m-2

49 mW m-2

Figure 10: Example of heat flow calculation for Hole 747A, Leg 120. Left: sediment temperatures; center:thermal resistance based on continuous thermal conductivity approach (Fig. 8), dotted line: average, dashedline: linear, solid line: porosity related; right: Bullard Plot, heat flow is calculated individually for each tem-perature value (60 and 37 mW m-2) and from a linear regression of all data (dashed line; 49 mW m-2).


Pribnow, Kinoshita & Stein - 15 -

3. Thermal Data from Legs 101 - 180Thermal data for Legs 101 – 180 were compiled from ODP Initial Results (IR) Volumes

and the ODP data base at Texas A&M University (TAMU) in College Station, Texas. Thesedata include shipboard measurements of thermal conductivity and borehole measurements ofsediment temperatures.

3.1 Sediment TemperaturesFrom the first 80 ODP

Legs with 475 sites, reliablesediment temperatures weremeasured at 205 sites from 53Legs. For Legs 111, 121, 128 and135, sediment temperatures areavailable in figures only and hadto be scanned. Only raw datawere available for Legs 174, 175,177, and 178. The original tem-perature-time data of the meas-urements are available at TAMUand were used to recalculate theequilibrium value in a consistentmanner for a total of 55 sites (seeSection 2.2). A total of 993 individual temperaturevalues yields an average of 4.8 measurements per site(Figure 11). The maximum depth of available meas-urements is 550 mbsf. Temperatures range from-0.9 °C to 208 °C, and the average gradient is 179K km-1. Sea floor temperatures are measured in thedrill string by monitoring for several minutes at thecorresponding depth below rig floor. These values areof special interest because they define the temperaturegradient in the uppermost part of the sea floor. Forabout 30% of the sites, however, this attempt was notmade (or not reported) and sea floor temperatures hadto be determined by extrapolation of sediment tem-peratures. Of the total 993 temperature values, 145are from the seafloor, varying from –0.9 °C to+18.7 °C with an average of 4.2 °C. Figure 12 showsall sediment temperatures used in this study.

0 2 4 6 8 10 12 14 16 18 20 22number of individual temperature measurements

0

10

20

30

40

50

60

num

ber o

f site

s

Figure 11: Histogram of temperature measurements per site.

0 50 100 150 200 250

0

100

200

300

400

500

600

temperature (oC)

dept

h (m

bsf)

0.1 K/m

2.0 K/m0.5 K/m

gradient

Figure 12: Sediment temperatures fromLegs 101- 180 used for this study togetherwith example temperature gradients.

ODP Heat Flow Report


3.2 Shipboard Thermal ConductivityWe used ODP thermal conductivity data only

for sites with available and reliable sediment tem-peratures. For 15 sites (Legs 109, 111, 155), nomeasurements are reported and sediment conduc-tivity was estimated. About 2% of the available datawere lower than the thermal conductivity of seawater (0.6 W m-1 K-1) and therefore neglected. Atotal of 15477 thermal conductivity measurementswith a maximum depth of 1070 mbsf are used inthis study (Fig. 13). The data from 205 sites werefitted with the average approach (eq. 3) for 72 sites(35%), with the linear approach (eq. 5) for 88 sites(43%), and with the porosity approach (eq. 8) for 45sites (22%). 1.0 2.0 3.0

0

200

400

600

800

1000


dept

h (m

bsf)

Figure 13: Sediment thermal conductivityfrom shipboard measurements of Legs 101-180.


4. Recalculated Heat FlowHeat flow values were re-

ported in the IR volumes for 160sites from Legs 101-180 (i.e.only 78% of the sites with avail-able and reliable temperaturemeasurements). We recalculatedheat flow for all 205 sites in aconsistent manner (see Section2.3). Differences to the reportedvalues are related to (1) the cho-sen method to calculate heatflow, (2) consideration of allavailable temperature values inthis study (no elimination of so-called “obvious outliers“), and(3) the in-situ correction forlaboratory thermal conductivitymeasurements. The intention ofthis study is to provide compara-ble results by applying identicalprocedures to all sites. In specialcases, e.g. with fluid flow in thesediments or very high heat flow,this strategy can result in largedifferences to the reported val-ues, where specific conditionswere considered by the individ-ual scientists. In these cases, ourdata collection provides the op-portunity for other researchers toperform their own calculationsand corrections. Figure 14 showsa histogram of the relative differ-ences between reported and re-calculated heat flow values.

Recalculated heat flowvalues range from 5 mW/m2 to 13 W m-2. Figure 15 shows a histogram of the heat flow valuesless than 200 mW m-2 (90% of the data) with the most common values between 30 mW m-2

and 60 mW m-2.

-50 -40 -30 -20 -10 0 10 20 30 40 50relative difference of reported and recalculated heat flow in %

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Figure 15: Histogram of recalculated heat flow values less than200 mW/m2 (90% of the data).

Prib

Our heat flow values for the 205 ODP sites and the values from shallow sea floor meas-urements (Davis et al., 1997c) are shown in Figure 16. The quality of the recalculated heatflow values is evaluated by the following method:A Uncertainty of recalculated heat flow less than 10%

at least two sediment temperature values anda linear temperature gradient andsufficient number of thermal conductivity values

B Uncertainty of recalculated heat flow between 10% and 20%minor deviations from linear temperature gradient orinsufficient number of thermal conductivity values

C Uncertainty of recalculated heat flow larger than 20%only one sediment temperature value ortemperatures scanned from figures ormajor deviations from linear temperature gradient orno thermal conductivity values available orin-situ correction for thermal conductivity questionable

Of the total 205 heat flow sites, 93 were rated A, 55 were rated B, and 57 were rated C.

now, Kinoshita & Stein - 18 - ODP Heat Flow Report

Figure 16: ODP sites with recalculated heat flow (white circles) in comparison with shallow sea floor measu-rements contoured on a 5°x5° grid. This page: North- and South Pole areas; next page: global view. Whiteareas indicate no measurements in a grid. Solid black lines are plate boundaries.

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5. Available DataThe data used in this study and our results are made available in various formats: ASCII,

PDF and MS EXCEL97 files on the included CD.

5.1 Temperature DataThe results of individual sea floor and sediment temperature measurements are listed as

tab-delimited ASCII text in ODPTemp.txt. The three columns are (1) site, (2) depth in metersbelow sea floor (mbsf), and (3) extrapolated equilibrium temperature in °C.

5.2 Thermal Conductivity and Resistivity DataIf available, thermal properties of sediments are listed for sites with sediment tempera-

tures as tab-delimited ASCII text in ODPThC.txt. The six columns are (1) site, (2) depth inmeters below sea floor (mbsf), (3) shipboard thermal conductivity in W m-1 K-1, (4) in-situcorrected thermal conductivity in W m-1 K-1 (eq. 13), and (5) cummulative thermal resistancein m2 K W-1 (Section 2.3.2).

5.3 Heat Flow CalculationsHeat flow calculations are provided as MS EXCEL97 files. Table 1 shows an example.

The top of the left three columns contain depth z (mbsf: meters below sea floor), the individ-ual temperature values (T(z) in °C), and thermal resistance (tr(z) in m2 K W-1) calculated ac-cording to the thermal conductivity approach used (Section 2.3.2). In the fifth column, heatflow is calculated for each interval of temperature values as a function of depth (q(z) inmW m-2) from the slope of temperature versus thermal resistance (Section 2.3.5). The top ofcolumn six shows the average heat flow for this site (q) calculated from a linear regression ofall temperature versus thermal resistance values from columns two and three. Below, the cor-relation coefficient (correl q) is given. In the center of column six, the temperature gradient(gT) is calculated from columns one and two together with a correlation coefficient (correlgT). In addition, the sea floor temperature is extrapolated from the given sediment tempera-tures (T0 from intercept in °C), and the slope of heat flow versus depth (q(z), column five) iscalculated. In the lower part of the spreadsheet, shipboard thermal conductivity values (col-umn two) are corrected for in-situ conditions (eq. 13) and then fitted with an average, linearregression or porosity-related approach (Sections 3.2.2.1, 3.2.2.2, and 3.2.2.3, respectively).The fitting results are listed below therm con in column seven. These values are used to cal-culate the cummulative thermal resistance (therm res in column five and tr(z) at the top ofcolumn three). Further below to the right the parameters necessary to perform the in-situ cor-rections (insitu corr.) are listed (eq. 13): water depth (taken from IR volumes), sediment den-sity (generally assumed to be 1.8 g cm-3), sea floor temperature (taken from top of columntwo), mean gradient (taken from gT in column six) and laboratory temperatures during ther-mal conductivity measurements (generally assumed to be 15 °C).

Pribnow,

Table 1: Example of provided MS EXCEL 97 spreadsheet for individual heat flow calculations.

mbsf T(z) tr(z) T0 from intercept slope of q(z)q(z) q

(mW/m2)0.00 1.80 0.00 418 -15.35

57.20 20.40 49.55 375 correl q 36608.767.60 26.90 58.15 756 0.99

gT (K/km)356

correl gT0.99

k insitu fit therm res therm con0.00 1.050 0.000.40 1.06 1.03 1.053 0.09 A0.50 1.03 1.00 1.054 0.66 1.231.10 0.90 0.87 1.057 0.66 B1.10 1.06 1.03 1.057 1.42 0.221.90 0.98 0.95 1.063 1.42 C1.90 1.05 1.02 1.063 2.08 252.60 1.09 1.06 1.067 2.082.60 1.11 1.08 1.067 2.833.40 1.27 1.23 1.072 3.113.70 1.30 1.27 1.073 3.48 insitu corr4.10 1.20 1.17 1.076 4.234.90 1.01 0.98 1.080 4.50 water depth (m) 2444.005.20 1.03 1.00 1.082 4.87 sediment dens. (g/cm3) 1.805.60 1.11 1.08 1.084 5.61 T bottom water 1.806.40 1.16 1.13 1.088 5.61 mean gradient 0.366.40 1.11 1.08 1.088 5.89 lab T 15.006.70 1.03 1.01 1.090 6.997.90 1.10 1.07 1.09 6.99

Kinoshita & Stein - 21 - ODP Heat Flow Report

P

5.4 Bullard PlotsThe spreadsheets discussed in Section 5.3 are used to create Bullard Plots for each site

(Section 2.3.1 and Figure 10). All Bullard Plots are available in PDF format in Bullards.pdf.For each site, three graphs are shown (Figure 17): (1) extrapolated equilibrium temperaturesversus depth with linear regression, (2) in-situ corrected shipboard thermal conductivity ver-sus depth together with appropriate fit, and (3) temperature versus cummulative thermal re-sistance with linear regression. In most but not all cases, the depth axes of the first two graphshave identical limits. (Note that the vertical axis of the third graph is not depth.)

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Figure 17: Example of a Bullard Plot; left: extrapolated equilibrium temperatures versus depth (diamonds,connected by dotted line) with linear regression (solid line); center: in-situ corrected shipboard thermal con-ductivity measurements (dots) with appropriate fit (line): right: temperature versus cummulative thermalresistance (squares, connected by dotted line) with linear regression (solid line).



5.5 SummaryThe results of this synthesis are summarized in three files.

5.5.1 Summary of Temperature DataThe summarized temperature data is available as tab-delimitted ASCII format in

sum_tmp.txt and in PDF format in sum_tmp.pdf. The columns are: (1) leg number, (2) sitenumber, (3) latitude and (4) longitude of the site (in degrees, N positive, S negative, E posi-tive, W negative), (5) temperature tools used (see Section 2.2), (6) number of individual tem-perature measurements, (7) maximum depth of measurements (in mbsf), and (8) temperaturegradient (in K km-1).5.5.2 Summary of Thermal Conductivity Data

The summarized thermal conductivity data is available as tab-delimitted ASCII formatin sum_thc.txt and in PDF format in sum_thc.pdf. The columns are: (1) leg number, (2) sitenumber, (3) latitude and (4) longitude of the site (in degrees, N positive, S negative, E posi-tive, W negative). The next columns provide the results of one appropriate thermal conduc-tivity fit: average approach (Section 2.3.2.1): column (5) lists the average thermal conductivitykav (eq. 3) in W m-1 K-1; or linear approach (Section 2.3.2.2): column (6) lists the sea floorthermal conductivity k(0) in W m-1 K-1 and column (7) the slope in W m-2 K-1 as a result of alinear regression (eq. 5); or the porosity-related approach (Section 2.3.2.3): column (8) liststhe matrix thermal conductivity kmat in W m-1 K-1, column (9) the sediment porosity at the seafloor phi(0), and column (10) the characteristic depth D in mbsf from the fit to equations (7)and (8).5.5.3 Summary of Heat Flow Data

The summarized heat flow data is available as tab-delimitted ASCII format insum_hf.txt and in PDF format in sum_hf.pdf. The columns are: (1) leg number, (2) site num-ber, (3) latitude and (4) longitude of the site (in degrees, N positive, S negative, E positive, Wnegative), (5) reported heat flow in mW m-2 (if available), (6) recalculated heat flow inmW m-2, (7) quality rating, and (8) comments, e.g. explanation for a rating lower than A. Thecomments are k(z) insuff: not enough thermal conductivity measurements available, k(z) as-sumed: thermal conductivity was estimated due to lack of available measurements, k insitu:the applied in-situ correction for shipboard thermal conductivity measurements (eq. 12) isquestionable due to exceptionally high temperatures, only 1 T: only one sediment temperaturemeasurement available, T scanned from figure: temperature values were only available as fig-ure in IR volumes and had to be scanned, T new: equilibrium temperatures have been re-extrapolated (Section 2.2), var. gradT: medium to large variations in the temperature gradient,flow?: variation in temperature gradient suggests possible influence of fluid flow.

Acknowledgements. We are most thankful to scientits and staff of ODP, Tamu, and LDEOfor their help. This work was supported by NSF grant OCE-9634140 and DFG grant Pr 471/2.


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